Math Help Forum: Noraml distribution question...

Supppose the life span of a battery is normally distributed. The useful life of the battery has a mean of 600 hours and standard deviation of 40 hours. Find the probability that a battery chosen at random will last between 600 and 680 hours. I need a little help getting going on this one. I know it is somewhere between .45 and .55, but am unsure how to get there. Any help is greatly appreciated.

Originally Posted by bemidjibasser

Supppose the life span of a battery is normally distributed. The useful life of the battery has a mean of 600 hours and standard deviation of 40 hours. Find the probability that a battery chosen at random will last between 600 and 680 hours. I need a little help getting going on this one. I know it is somewhere between .45 and .55, but am unsure how to get there. Any help is greatly appreciated.

Let represent the life span of a battery. and

We are looking for

Incorporating the z-score, we see that .

You can find this solution in standard normal distribution tables. If you have a TI 83 or higher, you can use the normalcdf command to give you your probability. It should be about .4772.